On graphs supported by line sets

Vida Dujmović, William Evans, Stephen G Kobourov, Giuseppe Liotta, Christophe Weibel, Stephen Wismath

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

For a set S of n lines labeled from 1 to n, we say that S supports an n-vertex planar graph G if for every labeling from 1 to n of its vertices, G has a straight-line crossing-free drawing with each vertex drawn as a point on its associated line. It is known from previous work [4] that no set of n parallel lines supports all n-vertex planar graphs. We show that intersecting lines, even if they intersect at a common point, are more "powerful" than a set of parallel lines. In particular, we prove that every such set of lines supports outerpaths, lobsters, and squids, none of which are supported by any set of parallel lines. On the negative side, we prove that no set of n lines that intersect in a common point supports all n-vertex planar graphs. Finally, we show that there exists a set of n lines in general position that does not support all n-vertex planar graphs.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages177-182
Number of pages6
Volume6502 LNCS
DOIs
StatePublished - 2011
Event18th International Symposium on Graph Drawing, GD 2010 - Konstanz, Germany
Duration: Sep 21 2010Sep 24 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6502 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other18th International Symposium on Graph Drawing, GD 2010
CountryGermany
CityKonstanz
Period9/21/109/24/10

Fingerprint

Labeling
Line
Graph in graph theory
Planar graph
Vertex of a graph
Intersect
SQUID
Support Point
Straight Line

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Dujmović, V., Evans, W., Kobourov, S. G., Liotta, G., Weibel, C., & Wismath, S. (2011). On graphs supported by line sets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6502 LNCS, pp. 177-182). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6502 LNCS). https://doi.org/10.1007/978-3-642-18469-7_16

On graphs supported by line sets. / Dujmović, Vida; Evans, William; Kobourov, Stephen G; Liotta, Giuseppe; Weibel, Christophe; Wismath, Stephen.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6502 LNCS 2011. p. 177-182 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6502 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Dujmović, V, Evans, W, Kobourov, SG, Liotta, G, Weibel, C & Wismath, S 2011, On graphs supported by line sets. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 6502 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6502 LNCS, pp. 177-182, 18th International Symposium on Graph Drawing, GD 2010, Konstanz, Germany, 9/21/10. https://doi.org/10.1007/978-3-642-18469-7_16
Dujmović V, Evans W, Kobourov SG, Liotta G, Weibel C, Wismath S. On graphs supported by line sets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6502 LNCS. 2011. p. 177-182. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-18469-7_16
Dujmović, Vida ; Evans, William ; Kobourov, Stephen G ; Liotta, Giuseppe ; Weibel, Christophe ; Wismath, Stephen. / On graphs supported by line sets. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6502 LNCS 2011. pp. 177-182 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{32d7511d57984e718418b46c662867cf,
title = "On graphs supported by line sets",
abstract = "For a set S of n lines labeled from 1 to n, we say that S supports an n-vertex planar graph G if for every labeling from 1 to n of its vertices, G has a straight-line crossing-free drawing with each vertex drawn as a point on its associated line. It is known from previous work [4] that no set of n parallel lines supports all n-vertex planar graphs. We show that intersecting lines, even if they intersect at a common point, are more {"}powerful{"} than a set of parallel lines. In particular, we prove that every such set of lines supports outerpaths, lobsters, and squids, none of which are supported by any set of parallel lines. On the negative side, we prove that no set of n lines that intersect in a common point supports all n-vertex planar graphs. Finally, we show that there exists a set of n lines in general position that does not support all n-vertex planar graphs.",
author = "Vida Dujmović and William Evans and Kobourov, {Stephen G} and Giuseppe Liotta and Christophe Weibel and Stephen Wismath",
year = "2011",
doi = "10.1007/978-3-642-18469-7_16",
language = "English (US)",
isbn = "9783642184680",
volume = "6502 LNCS",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "177--182",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}

TY - GEN

T1 - On graphs supported by line sets

AU - Dujmović, Vida

AU - Evans, William

AU - Kobourov, Stephen G

AU - Liotta, Giuseppe

AU - Weibel, Christophe

AU - Wismath, Stephen

PY - 2011

Y1 - 2011

N2 - For a set S of n lines labeled from 1 to n, we say that S supports an n-vertex planar graph G if for every labeling from 1 to n of its vertices, G has a straight-line crossing-free drawing with each vertex drawn as a point on its associated line. It is known from previous work [4] that no set of n parallel lines supports all n-vertex planar graphs. We show that intersecting lines, even if they intersect at a common point, are more "powerful" than a set of parallel lines. In particular, we prove that every such set of lines supports outerpaths, lobsters, and squids, none of which are supported by any set of parallel lines. On the negative side, we prove that no set of n lines that intersect in a common point supports all n-vertex planar graphs. Finally, we show that there exists a set of n lines in general position that does not support all n-vertex planar graphs.

AB - For a set S of n lines labeled from 1 to n, we say that S supports an n-vertex planar graph G if for every labeling from 1 to n of its vertices, G has a straight-line crossing-free drawing with each vertex drawn as a point on its associated line. It is known from previous work [4] that no set of n parallel lines supports all n-vertex planar graphs. We show that intersecting lines, even if they intersect at a common point, are more "powerful" than a set of parallel lines. In particular, we prove that every such set of lines supports outerpaths, lobsters, and squids, none of which are supported by any set of parallel lines. On the negative side, we prove that no set of n lines that intersect in a common point supports all n-vertex planar graphs. Finally, we show that there exists a set of n lines in general position that does not support all n-vertex planar graphs.

UR - http://www.scopus.com/inward/record.url?scp=79952268624&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952268624&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-18469-7_16

DO - 10.1007/978-3-642-18469-7_16

M3 - Conference contribution

AN - SCOPUS:79952268624

SN - 9783642184680

VL - 6502 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 177

EP - 182

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -